Slides: https://www.andreashandel.com/presentations/
2025-10-13
Example of BioNTech/Pfizer COVID Vaccine
Claim: Knowing in more detail how dose impacts host response following vaccination might help optimize vaccines.
Exponential decay model: \[ y_1(t) = \frac{p_1}{1+e^{(-g_1*(t-k_1))}}e^{-d_1*t} \]
Power-law decay model: \[ y_2(t) = \frac{p_2}{1+e^{(-g_2*((t+1)-k_2))}}(t+1)^{-d_2} \]
Hierarchical/mixed-effects modeling framework
For this project, the goals were to:
We focused on viral infections as a stand-in for live attenuated vaccines.
\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I \\ \textrm{Dead cells} \qquad \dot{D} & = d_I I \\ \textrm{Virus} \qquad \dot{V} & = \frac{pI}{1+s_F F} - (d_V V + k^{'}_{A}A + b^{'} U)V\\ \textrm{Innate response} \qquad \dot{F} & = p_F - d_F F + \frac{g_F (F_{max} - F)V}{V+h_V} \\ \textrm{B cells} \qquad \dot{B} & = \frac{F V}{FV+h_F} g_B B \\ \textrm{Antibodies} \qquad \dot{A} & = r_A B - d_A A - k_{A}AV \\ \end{aligned} \]
We want to know protection. We can map antibodies to it. We use this relation: \(P=1−1/(1+e^{k_1(log(A)−k_2)})\)
We want to know morbidity (side effects/symptoms). We can map the innate response to it. \[ M = \int \frac{aF^c}{b+F^c} \]
Conceptual model suggests that protection (and morbidity) could be peaked.
For teaching (stable):
For research (WIP):
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